I'm still early in the game, but I stopped for a few minutes to finish up the Augmented Reality Training challenges. Completing the first set of them earned me a new gadget.

However, a bunch more "Advanced" challenges unlocked, and I'm absolutely terrible at them. I've considered just leaving them for now, and coming back when I have more experience, but I'm worried that perhaps something useful will unlock if I can finish them off now.

Is there any reason to finish up these challenges now, or can I safely move on with the game?

You don't get anything else in regards to gameplay for completing the Advanced Augmented Reality Training. For completing them all, you get the AR Knight achievement. Unfortunately, completing all of the ART sequences is a Sidequest, so in order to get the Perfect Knight - Day 2 achievement, you'll have to complete them.